Since a single pickup can be used for both a compact disk and an optical video disk, an optical disk player capable of playing both types of disks has become popular. In a conventional disk player of such kind, a compact disk or a video disk is placed on a rest, and the rest is then driven by a motor to load the disk onto a turntable. The diameter of the turntable is made small so that the turntable does not hinder the movement of the pickup of the player. Although the small diameter of the turntable does not cause a problem for the compact disk which also has a small diameter, the small diameter of the turntable does cause a problem for the video disk which has a relatively large diameter. More particularly, the video disk is likely to warp due to its own weight if it is left unrotated on the small diameter turntable for a long period of time. In order to prevent the video disk from warping due to its own weight, it has been proposed to use a motor for vertically moving the video disk from the turntable. This motor is provided in addition to the loading motor (i.e., the motor for loading the disk onto the turntable). This additional motor serves to lift a rest (which supports the video or compact disk) to the same elevational position as in a disk discharge mode, to thereby hold the disk in that position during a stand-by mode of operation (i.e., the mode for waiting for a next command to be given). However, this previous solution to the warping problem results in a complicated construction of the disk player, which necessarily increases the cost of the machine. This previous solution has the further shortcoming of requiring a longer time to execute the next command after it is given, due to the fact that the compact or video disk is positioned far from the turntable during the stand-by mode. Thus, there is a need in the art for a disk record/playback machine which overcomes the aforementioned drawbacks.